In order to find the x and y intercepts of a graph, we need to remember that we’re looking for where the graph crosses the x and y axes. If the graph crosses the x-axis, then that point has a y-coordinate of 0 since all points on the x-axis have y-coordinate 0. To find an x-intercept, merely substitute 0 for y, and then solve for x. If the graph crosses the y-axis, then that point has an x-coordinate of 0 since all points on the y-axis have x-coordinate 0. To find the y-intercepts, we set x equal to zero and solve for y. Thus, if , the y-intercept of the graph is . Note that we usually just say that is the y-intercept, rather than more accurately saying that is the y-intercept.

Example 1

Find the x and y intercepts of the graph of .

Solution1

The y-intercept is

To find the x-intercept. Substitute 0 for y and solve for x:

The y-intercept is at the point (0, -7) and the x-intercept is ( , 0).